Delayed-acceptance approximate Bayesian computation Markov chain Monte Carlo: faster simulation using a surrogate model

The thesis introduces an innovative way of decreasing the computational cost of approximate Bayesian computation (ABC) simulations when implemented via Markov chain Monte Carlo (MCMC). Bayesian inference has enjoyed incredible success since the beginning of 1990’s thanks to the re-discovery of MCMC procedures, and the availability of performing personal computers. ABC is today the most famous strategy to perform Bayesian inference when the likelihood function is analytically unavailable. However, ABC procedures can be computationally challenging to run, as they require frequent simulations from the data-generating model. In this thesis we consider learning a so-called "surrogate model", one that is cheaper to simulate from, compared to the assumed data-generating model, and in this manner save computational time. The strategy implemented is known in MCMC literature as "delayed acceptance MCMC", however to the best of our knowledge has not been previously adapted into an ABC framework. Simulation studies consider the approach on two different models, producing Gaussian data and g-and-k distributed data, respectively. For the most challenging example we observed that our approach, consisting in a delayed-acceptance ABC algorithm, led to a 20-folds acceleration in the MCMC sampling, compared to a standard ABC-MCMC algorithm